As a new kind of highly compact and efficient micro-channel heat exchanger, the printed circuit heat exchanger (PCHE) is a promising candidate satisfying the heat exchange requirements of liquefied natural gas (LNG) vaporization at low and high pressure. The effects of airfoil fin arrangement on heat transfer and flow resistance were numerically investigated using supercritical liquefied natural gas (LNG) as working fluid. The thermal properties of supercritical LNG were tested by utilizing the REFPROF software database. Numerical simulations were performed using FLUENT. The inlet temperature of supercritical LNG was 121 K, and its pressure was 10.5 MPa. The reference mass flow rate of LNG was set as 1.22 g/s for the vertical pitch Lv = 1.67 mm and the staggered pitch Ls = 0 mm, with the Reynolds number of about 3750. The SST k-ω model was selected and verified by comparing with the experimental data using supercritical liquid nitrogen as cold fluid. The airfoil fin PCHE had better thermal-hydraulic performance than that of the straight channel PCHE. Moreover, the airfoil fins with staggered arrangement displayed better thermal performance than that of the fins with parallel arrangement. The thermal-hydraulic performance of airfoil fin PCHE was improved with increasing Ls and Lv. Moreover, Lv affected the Nusselt number and pressure drop of airfoil fin PCHE more obviously. In conclusion, a sparser staggered arrangement of fins showed a better thermal-hydraulic performance in airfoil fin PCHE.